CN116614201A - Polarization code decoding method for correcting insertion and deletion errors - Google Patents
Polarization code decoding method for correcting insertion and deletion errors Download PDFInfo
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- CN116614201A CN116614201A CN202310520220.6A CN202310520220A CN116614201A CN 116614201 A CN116614201 A CN 116614201A CN 202310520220 A CN202310520220 A CN 202310520220A CN 116614201 A CN116614201 A CN 116614201A
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- 238000003780 insertion Methods 0.000 title claims abstract description 46
- 230000037431 insertion Effects 0.000 title claims abstract description 46
- 238000012217 deletion Methods 0.000 title claims abstract description 31
- 230000037430 deletion Effects 0.000 title claims abstract description 31
- 238000000034 method Methods 0.000 title claims abstract description 29
- 230000010287 polarization Effects 0.000 title description 14
- 230000005540 biological transmission Effects 0.000 claims abstract description 16
- 238000013138 pruning Methods 0.000 claims abstract description 3
- 230000007704 transition Effects 0.000 claims description 29
- 238000006467 substitution reaction Methods 0.000 claims description 8
- 241000169170 Boreogadus saida Species 0.000 claims 1
- 238000004422 calculation algorithm Methods 0.000 abstract description 11
- 238000012937 correction Methods 0.000 abstract description 5
- 238000012546 transfer Methods 0.000 abstract 2
- 238000004891 communication Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 239000000654 additive Substances 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 238000010295 mobile communication Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
Classifications
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0061—Error detection codes
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention discloses a polar code decoding method for correcting insertion and deletion errors, which comprises the following steps: for information bits of length KAnd mixing all-zero fixed bits with the length of N-K according to the preset information bits and the position indexes of the fixed bits to obtain a bit sequenceFor bit sequencesCoding to obtain a transmission sequence with a length of NTransmission sequenceGenerating a length N after IDS channel * Is a received sequence of (2)SC decoder based on weighted edit distance, correcting received sequenceIn an insertion and pruning error, outputting an estimate of the information sequenceThe invention aims at inserting and deleting-replacing channels, introduces drift amount into the recursive computation of channel transfer probability, improves the recursive structure of the traditional SC decoding algorithm, adopts weighted editing distance to measure the channel transfer probability, obtains good error correction performance and improves the accuracy of information transmission.
Description
Technical Field
The invention relates to the field of digital communication error control coding, in particular to a polar code decoding method for correcting insertion and deletion errors.
Background
Insertion and deletion errors are widely existed in various systems, for example, during information transmission, due to unstable sampling clock of a receiver in a communication system, the insertion or deletion errors can occur when a sampler is not adopted or is adopted, and the system is out of synchronization. Insertion and deletion errors may also occur in some storage devices, where factors such as manufacturing defects in the media cause the intended write window to be misaligned with the actual magnetic spot location, resulting in insertion and deletion errors. Systems with insertion and puncturing errors are memory, and a single insertion and puncturing error causes sudden replacement errors, severely damaging communication quality, which cannot be corrected by conventional polarization codes.
The polarization code is a channel code which is proposed by Arikan teaching based on a channel polarization theory, is the only channel code which is theoretically proved to reach the Shannon limit under a Binary discrete memory-free channel (Binary-Discrete Memoryless Channel, B-DMC) at present, has lower coding and decoding complexity, and has wide development prospect in the fields of new-generation mobile communication, satellite communication and the like. At present, the research of polarization codes mainly aims at binary memory-free channels, and the research of memory-free insertion and deletion channels is less.
In the prior art, tian Kuangda and the like propose a polar code decoding algorithm under a truncated channel, and only a truncated error can be corrected. Sun He et al propose error correction schemes that can correct the inserted and truncated-additive white gaussian noise channel model by improving the polar code decoding algorithm. In practical applications, the insertion and deletion errors often occur with a certain probability, i.e. there may be multiple insertion and deletion errors in the received sequence at the same time, and the number is unknown.
Disclosure of Invention
The invention provides a polar code decoding method for correcting insertion and deletion errors, which aims at insertion and deletion-substitution channels, introduces drift amount into recursive calculation of channel transition probability, improves the recursive structure of a traditional SC decoding algorithm, adopts weighted editing distance to measure the channel transition probability, obtains good error correction performance, improves the accuracy of information transmission, and is described in detail below:
a polar coding method to correct insertion and pruning errors, the method comprising:
for information bits of length KAnd the all-zero fixed bit with the length of N-K is mixed according to the preset information bit and the position index of the fixed bit to obtain a bit sequence +.>
For bit sequencesCoding to obtain a transmission sequence of length N>
Transmission sequenceGenerating a length N after IDS channel * Is>
SC decoder based on weighted edit distance, correctionReceiving a sequenceIs an insertion and deletion error in the output information sequence>
Wherein the SC decoder based on the weighted editing distance corrects the received sequenceIs an insertion and deletion error in the output information sequence>The method comprises the following steps:
computing a received sequenceAs the channel transition probability of layer 0;
recursively calculating channel transition probabilities by using the initialization information; and decoding and judging bit by bit according to the channel transition probability.
Wherein, the channel transition probability of the 0 th layer is:
wherein ,the i-th bit representing layer 0 +.>And subsequence->Weighted edit distance between, parameter P i 、P d and Ps Respectively represent the insertion of channelsErasure and substitution probability, transmission probability P t ＝1-P i -P d ，d i Is the drift amount of the i point.
Further, the recursively calculating the channel transition probability using the initialization information is:
for the ith bit of the kth e { n, n-1, …,1} layer, the index is represented by a set (m, j), where n=log 2 N，m∈{0,1,…,2 n-k -1}，j∈{0,1,…,2 k-1 -1}；
The following definitions are used in recursion:
a＝2 k ×m，b＝(m+1)×2 k ，
where k is the number of layers, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, c is the intermediate value between a and b, even representsElements with even medium index, odd represents +.>Elements with medium index odd;
if the index is even:
if the index is odd:
wherein ,representing an exclusive-or operation of two bits, +.>Expression sequence->Set d= { -D max ,…,-2,-1,0,1,2,…,d max Set b= {0,1}, d b 、d a 、d c Drift amounts respectively expressed as b point, a point and c point, +.> and />Representing the channel transition probability when the index is even or odd, respectively,/->Expression sequence->d max Represents the maximum drift amount +.>Sequence u representing the kth layer (k) (u a ,…,u a+2j+1 )，/>A+2j bit representing the kth layer,>representing the transition probability of the branch.
The bit-by-bit decoding and judgment according to the channel transition probability are as follows:
judging whether the ith bit is an information bit or a fixed bit, and if the ith bit is the fixed bit, using 0 as a judging result; otherwise, assuming that the estimates of the previous i-1 bits are all correct, determining based on likelihood ratiosIs the value of (1):
wherein set A represents an information bit channel index set, A c To represent a fixed set of bit channel indices,the decoding likelihood ratio of the ith bit is represented by the following formula:
the technical scheme provided by the invention has the beneficial effects that:
1. the invention adopts the polarization code to correct the insertion and deletion errors, improves the traditional SC decoding algorithm by introducing the drift amount, and obtains good error correction performance; the accuracy of information transmission is improved, the error rate is reduced, and the safety of channel transmission is ensured;
2. the invention expands the application of the polarization code in IDS channels, obtains remarkable performance gain and meets various requirements in practical application.
Drawings
FIG. 1 is a schematic diagram of a polar code encoding and decoding for correcting insertion and erasure errors according to the present invention;
FIG. 2 is a flow chart of SC decoding based on weighted edit distance used in the present invention;
fig. 3 is a schematic diagram of the drift amount recursive calculation when the code length n=8;
wherein, (a) is a recursive diagram of the SC decoding algorithm of the polarization code based on the weighted editing distance; (b) is a detailed operational diagram of a dotted rectangle.
FIG. 4 is a graph showing the performance simulation of the method provided by the present invention compared with the prior art.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below.
Aiming at an Insertion/Deletion-Substitution (IDS) channel, the embodiment of the invention provides a novel polarization code decoding method, and introduces drift quantity to correct Insertion and Deletion errors on the basis of a traditional continuous cancellation (Successive Cancellation, SC) decoding method and adopts weighted editing distance to measure the transition probability of the channel.
The embodiment of the invention designs a polarization code decoding method for correcting insertion and deletion errors under the framework of SC decoding, and compared with the traditional scheme, the embodiment of the invention has the following modifications:
the first, transmitted sequence passes through the insert, prune-substitute channel;
secondly, introducing drift amount in the calculation of the decoding algorithm, and correcting insertion and deletion errors;
third, the channel transition probability is calculated from the weighted edit distance.
Compared with the traditional SC decoding algorithm, the embodiment of the invention introduces the drift amount into the decoding algorithm to obtain excellent insertion and deletion error correction capability, and widens the application range of the polarization code.
The following describes a detailed description of a method for decoding a polar code for correcting insertion and deletion errors according to an embodiment of the present invention with reference to the accompanying drawings:
as shown in fig. 1, the method comprises the following four steps:
(1) For information bits of length KAnd all zero fixed bits of length N-KMixing according to the position indexes of the preset information bit and the fixed bit to obtain bit sequence +.>
(2) For bit sequencesCoding to obtain a transmission sequence of length N>
(3) Transmission sequenceGenerating a length N after IDS channel * Is>
(4) SC decoder based on weighted edit distance, correcting received sequenceIs an insertion and deletion error in the output information sequence>
Wherein, the step (4) comprises:
(4.1) computing the received sequenceIs set, the initialization information of (a) is set;
wherein the initialization information is used as the channel transition probability of the 0 th layer.
(4.2) recursively calculating channel transition probabilities using the initialization information;
(4.3) decoding and judging bit by bit according to the channel transition probability.
In specific decoding, a decision is 0 or 1 according to the transition probability of the recursion n layer.
The following describes the implementation process of the four steps respectively:
step (1) determining the position index of the fixed bits using gaussian approximation (known to those skilled in the art);
step (2) encoding includes constructing a generator matrix in the same manner as conventional encoding (known to those skilled in the art);
the transmission sequence in step (3)Generating a length N via an inserted and truncated-alternate channel * Is>The method comprises the following steps:
transmitting codeword x i Parameter P by inserting and puncturing-substitution channels i 、P d and Ps Respectively represent the insertion, deletion and substitution probabilities of the channels, and the transmission probability P t ＝1-P i -P d 。
Define state d i Is the drift amount of the point i, d i Equal to the transmitted bit x 0 To bit x to be transmitted i The number of insertions present in the sequence between them minus the number of deletions. d, d i The value taken from the set d= { -D max ,…,-2,-1,0,1,2,…,d max}. wherein di Totally 2d max +1 values, d max Is the maximum amount of drift.
Calculating the received sequence in step (4.1)The initialization information of (a) specifically includes:
let k=0, calculate the channel transition probability of layer 0.
wherein ,representation->And subsequence->The weighted editing distance is calculated by a dynamic programming method.
The step (4.2) of recursively calculating the channel transition probability by using the initialization information specifically includes:
(4.2.1) for the ith bit of the kth e { n, n-1, …,1} layer, its index can be represented by a set of (m, j), where n=log 2 N，m∈{0,1,…,2 n-k -1}，j∈{0,1,…,2 k-1 -1}。
The following definitions need to be used in recursion:
a＝2 k ×m，b＝(m+1)×2 k ，
where k is the number of layers, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, c is the intermediate value of a and b,sequence u representing the kth layer (k) (u a ,…,u a+2j+1 ) Even means->Elements with even medium indexOdd means +.>Elements with an odd index.
Based on the parity of the bit index, the channel transition probability can be calculated by the following two recursive formulas:
if the index is even:
conversely, if the index is odd:
wherein ,representing an exclusive-or operation of two bits, +.>Expression sequence->Set d= { -D max ,…,-2,-1,0,1,2,…,d max Set b= {0,1}, d b 、d a 、d c Drift amounts respectively expressed as b point, a point and c point, +.> and />Representing the channel transition probability when the index is even or odd, respectively,/->Representing sequencesd max Indicating the maximum amount of drift.
In the step (4.3), the steps of decoding and judging bit by bit according to the channel transition probability are specifically as follows:
the information source sequence is judged bit by bit according to the sequence, firstly, whether the ith bit is an information bit or a fixed bit is judged, and if the ith bit is the fixed bit, 0 is directly used as a judging result; otherwise, assuming that the estimates of the previous i-1 bits are all correct, determining based on likelihood ratiosIs the value of (1):
wherein set A represents an information bit channel index set, A c To represent a fixed set of bit channel indices,the decoding likelihood ratio of the ith bit is represented by the following formula:
the embodiment of the invention selects a polarization code with a code length N of 512 bits and a code rate of 0.5 as a special case, and introduces a polarization code decoding method for correcting insertion and deletion errors. In the simulation, the fixed bit position index is calculated by adopting a Gaussian approximation method, the coding algorithm is consistent with the traditional algorithm, the number I of maximum insertion errors of each bit in a channel is 2, and the number P of the maximum insertion errors of each bit in the channel is 2 i ＝P d Maximum drift d max ＝5。
Fig. 4 shows a plot of the frame error rate and bit error rate of the system as a function of the insertion/puncturing probability for the same substitution probability. Wherein the frame error rate is the number of error frames divided by the total number of transmitted frames, and the bit error rate is the number of error bits divided by the total number of transmitted bits. As can be seen from the figure, the system performance is significantly improved as the probability of insertion/deletion decreases. Meanwhile, under the same insertion/deletion probability, the traditional SC decoding method cannot be applied, and the method provided by the invention has lower frame error rate and bit error rate and shows obvious performance gain. This demonstrates that the polar decoding method of the present invention can effectively correct errors in the insertion/puncturing-substitution channel and has good error performance.
Those skilled in the art will appreciate that the drawings are schematic representations of only one preferred embodiment, and that the above-described embodiment numbers are merely for illustration purposes and do not represent advantages or disadvantages of the embodiments.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (5)
1. A method of polar coding to correct insertion and pruning errors, the method comprising:
for information bits of length KAnd the all-zero fixed bit with the length of N-K is mixed according to the preset information bit and the position index of the fixed bit to obtain a bit sequence +.>
For bit sequencesCoding to obtain a transmission sequence of length N>
Transmission sequenceGenerating a length N after IDS channel * Is>
SC decoder based on weighted edit distance, correcting received sequenceIs an insertion and deletion error in the output information sequence>
2. The method for decoding polar codes for correcting insertion and deletion errors as set forth in claim 1 wherein the weighted edit distance-based SC decoder corrects the received sequenceIs an insertion and deletion error in the output information sequence>The method comprises the following steps:
computing a received sequenceAs the channel transition probability of layer 0;
recursively calculating channel transition probabilities by using the initialization information; and decoding and judging bit by bit according to the channel transition probability.
3. The method for decoding a polar code for correcting an insertion and puncturing error according to claim 2, wherein the channel transition probability of the 0 th layer is:
wherein ,the i-th bit representing layer 0 +.>And subsequence->Weighted edit distance between, parameter P i 、P d and Ps Respectively represent the insertion, deletion and substitution probabilities of the channels, and the transmission probability P t ＝1-P i -P d ，d i Is the drift amount of the i point.
4. The method for decoding a polar code for correcting an insertion and deletion error as set forth in claim 2 wherein said recursively calculating channel transition probabilities using initialization information is:
for the ith bit of the kth e { n, n-1, …,1} layer, the index is represented by a set (m, j), where n=log 2 N，m∈{0,1,…,2 n-k-1 }，j∈{0,1,…,2 k-1 -1}；
The following definitions are used in recursion:
a＝2 k ×m，b＝(m+1)×2 k ，
where k is the number of layers, m is the index of the block where the bit is located, a is the upper bound of the block, b is the lower bound of the block, c is the intermediate value between a and b, even representsElements with even medium index, odd represents +.>Elements with medium index odd;
if the index is even:
if the index is odd:
wherein ,representing an exclusive-or operation of two bits, +.>Expression sequence->Set d= { -D max ,…,-2,-1,0,1,2,…,d max Set b= {0,1}, d b 、d a 、d c Drift amounts respectively expressed as b point, a point and c point, +.>Andrepresenting the channel transition probability when the index is even or odd, respectively,/->Expression sequence->d max Represents the maximum drift amount +.>Sequence u representing the kth layer (k) (u a ,…,u a+2j+1 )，/>A+2j bit representing the kth layer,>representing the transition probability of the branch.
5. The method for decoding a polar code for correcting an insertion and puncturing error according to claim 2, wherein the decoding and deciding are performed bit by bit according to a channel transition probability:
judging whether the ith bit is an information bit or a fixed bit, and if the ith bit is the fixed bit, using 0 as a judging result; otherwise, assuming that the estimates of the previous i-1 bits are all correct, determining based on likelihood ratiosIs the value of (1):
wherein set A represents an information bit channel index set, A c To represent fixed bit channel index sets，The decoding likelihood ratio of the ith bit is represented by the following formula:
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